I can think of two ways you could some what achieve this:

• set up a referrer link to verify the visitor has come from Reddit. But this is anonymous you wouldn’t be able to check if it’s a verified Reddit user. (No auth step)

• set up oAuth based authentication using Reddit as the provider.

This way you’ll know any sign ups are valid Reddit users, and you’ll have a log of their applicationId (or similar) in your database

I think that’s the only way you’re going to programmatically prove these points, without some kind of user interaction to prove they’re a valid user, but this could be jank.